The effort to get occultism into Litvak Yeshivas is mainly because they are the gold standard of what qualifies as legitimate and authentic Torah.
Thus you can find elements of the occult in even well known Litvak Yeshivas. the only one that I know excludes all these elements rigorously is the yeshiva of Rav Zilverman in the Old City of Jerusalem which goes strictly by the Gra. I was pretty friendly with the rosh yeshiva there already for about 26 years and though I did not learn there myself I have been pretty well impressed with the place. The name is not so well known, but just for the record the name is Aderet Eliyahu.
Th great yeshivas like Ponovitch and Brisk are, as a rule, places where you can get into only f you already know how to learn. But Rav Zilverman's place starts at beginner levels. But there is also Machon Meir which I think is Mizrachi [Religious Zionist] that has a very good reputation.
I should mention that I have heard there are other start-up places that go by the Gra.